Translate Verbal Statements to Mathematical Expressions

Learning Outcomes

  • Express verbal statements as mathematical expressions

Translate word problems into expressions

To solve a word problem, you often need to translate a verbal expression into a mathematical expression. In the following table are some key words which correspond to common mathematical operations and relations.

Addition + sum, total, together, more than, increased by, …
Subtraction – difference, less than, decreased by, …
Multiplication * product, double, half, percent of, …
Equality = is, is the same as, is not different from, …

Example

Verbal Statement

Mathematical Statement
The sum of a number and 5 is 12 n+5=12
A number decreased by 5 is 12 n-5=12
Half of a number is 12 12n=12
The total of a number and 7 is the same as twice the number n+7=2n

In this example video, we show how to translate more words into mathematical expressions.

For more examples of how to translate verbal statements into algebraic statements, watch the following video.

Try It

Translate verbal statements involving inequalities into expressions

Often we are interested in how a quantity compares to a particular value. For example, if more than 50% of voters vote in favor of a proposal, the proposal passes and is adopted. If we let [latex]p[/latex] represent the proportion of voters who will vote in favor of a proposal, we can express the outcome “the proposal passes” as “[latex]p[/latex] > 0.5.” Any value of [latex]p[/latex] which is more than 0.5 satisfies this inequality.

The table below shows the relationships between possible verbal statements about the relationship between a variable [latex]x[/latex] and a constant [latex]k[/latex], and the corresponding mathematical statement.

Verbal Statement: x is…

Mathematical Statement
greater than or equal to [latex]k[/latex]
at least [latex]k[/latex]
not more than [latex]k[/latex]		  [latex]x \geq k[/latex]
less than or equal to [latex]k[/latex]
at most [latex]k[/latex]
not more than [latex]k[/latex]		  [latex]x \leq k[/latex]
less than [latex]k[/latex]
below [latex]k[/latex]
fewer than [latex]k[/latex]		  [latex]x
greater than [latex]k[/latex]
more than [latex]k[/latex]
above [latex]k[/latex]		 [latex]x>k[/latex]
equal to [latex]k[/latex]
is [latex]k[/latex]
exactly [latex]k[/latex]
the same as [latex]k[/latex]		 [latex]x=k[/latex]
not equal to [latex]k[/latex]
not [latex]k[/latex]
different from [latex]k[/latex]		 [latex]x \neq k[/latex]

EXAMPLE: EXPRESS A VERBAL STATEMENT INVOLVING INEQUALITY AS A MATHEMATICAL STATEMENT

Write the following as a mathematical statement, using [latex]x[/latex] for the variable.

The number of tries is no more than 12.

EXAMPLE: EXPRESS A VERBAL STATEMENT INVOLVING INEQUALITY AS A MATHEMATICAL STATEMENT

Write the following as a mathematical statement, using [latex]x[/latex] for the variable.

The number of hearts is fewer than 5.

Some verbal statements involve compound inequalities. That is, two inequalities must both be satisfied.

EXAMPLE: EXPRESS A VERBAL STATEMENT INVOLVING INEQUALITY AS A MATHEMATICAL STATEMENT

Write the following as a mathematical statement, using [latex]x[/latex] for the variable.

The number of defects is at least 1, but no more than 5.